。
She wants to go abroad to study music.
Literal
She [topic-は] music [object-を] learn [for-ため] abroad [to-へ] want-to-go [quotative-と] is-thinking.
Three flavor choices stack here. 学ぶ ('to learn, to study') is a touch more academic and aspirational than the everyday 勉強する; ~ため without に sounds slightly more written or compact than the more conversational ~ために; and ~たいと思っている (literally 'is thinking that wants to') is the standard polite shape for reporting someone else's third-person desire — the speaker doesn't have direct access to her wishes, so they're framed as reported thinking.